{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T03:07:11Z","timestamp":1791515231009,"version":"4.3.4"},"reference-count":99,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,6,25]],"date-time":"2023-06-25T00:00:00Z","timestamp":1687651200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,6,25]],"date-time":"2023-06-25T00:00:00Z","timestamp":1687651200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Engineering with Computers"],"published-print":{"date-parts":[[2024,4]]},"DOI":"10.1007\/s00366-023-01848-1","type":"journal-article","created":{"date-parts":[[2023,6,25]],"date-time":"2023-06-25T05:02:01Z","timestamp":1687669321000},"page":"1177-1216","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Dynamic crack propagation in anisotropic solids under non-classical thermal shock"],"prefix":"10.1007","volume":"40","author":[{"given":"Seyed Hadi","family":"Bayat","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7959-6078","authenticated-orcid":false,"given":"Mohammad Bagher","family":"Nazari","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,6,25]]},"reference":[{"key":"1848_CR1","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4614-0493-4","volume-title":"Heat waves","author":"B Straughan","year":"2011","unstructured":"Straughan B (2011) Heat waves. Springer Science & Business Media, New York"},{"issue":"5","key":"1848_CR2","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1016\/0022-5096(67)90024-5","volume":"15","author":"H Lord","year":"1967","unstructured":"Lord H, Shulman Y (1967) A generalized dynamical theory of thermoelasticity. J Mech Phys Solids 15(5):299\u2013309","journal-title":"J Mech Phys Solids"},{"issue":"1","key":"1848_CR3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF00045689","volume":"2","author":"AE Green","year":"1972","unstructured":"Green AE, Lindsay KA (1972) Thermoelasticity. J Elast 2(1):1\u20137","journal-title":"J Elast"},{"issue":"2","key":"1848_CR4","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1080\/01495739208946136","volume":"15","author":"AE Green","year":"1992","unstructured":"Green AE, Naghdi PM (1992) On undamped heat waves in an elastic solid. J Therm Stresses 15(2):253\u2013264","journal-title":"J Therm Stresses"},{"issue":"3","key":"1848_CR5","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/BF00044969","volume":"31","author":"AE Green","year":"1993","unstructured":"Green AE, Naghdi PM (1993) Thermoelasticity without energy dissipation. J Elast 31(3):189\u2013208","journal-title":"J Elast"},{"issue":"3","key":"1848_CR6","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1080\/01495730601130919","volume":"30","author":"SK Choudhuri","year":"2007","unstructured":"Choudhuri SK (2007) On a thermoelastic three-phase-lag model. J Therm Stresses 30(3):231\u2013238","journal-title":"J Therm Stresses"},{"issue":"3","key":"1848_CR7","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1080\/01495739.2010.545736","volume":"34","author":"A Zamani","year":"2011","unstructured":"Zamani A, Hetnarski RB, Eslami MR (2011) Second sound in a cracked layer based on Lord-Shulman theory. J Therm Stresses 34(3):181\u2013200","journal-title":"J Therm Stresses"},{"key":"1848_CR8","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1016\/j.tafmec.2018.02.007","volume":"95","author":"V Esmati","year":"2018","unstructured":"Esmati V, Nazari MB, Rokhi MM (2018) Implementation of XFEM for dynamic thermoelastic crack analysis under non-classic thermal shock. Theoret Appl Fract Mech 95:42\u201358","journal-title":"Theoret Appl Fract Mech"},{"key":"1848_CR9","doi-asserted-by":"crossref","DOI":"10.1016\/j.tafmec.2022.103557","volume":"122","author":"SH Bayat","year":"2022","unstructured":"Bayat SH, Nazari MB (2022) Dynamic crack propagation under generalized thermal shock based on Lord-Shulman model. Theoret Appl Fract Mech 122:103557","journal-title":"Theoret Appl Fract Mech"},{"key":"1848_CR10","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1016\/j.engfracmech.2017.12.039","volume":"191","author":"NR Zarmehri","year":"2018","unstructured":"Zarmehri NR, Nazari MB, Rokhi MM (2018) XFEM analysis of a 2D cracked finite domain under thermal shock based on Green-Lindsay theory. Eng Fract Mech 191:286\u2013299","journal-title":"Eng Fract Mech"},{"issue":"5","key":"1848_CR11","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1080\/01495739.2019.1571971","volume":"42","author":"M Shahsavan","year":"2019","unstructured":"Shahsavan M, Nazari MB, Rokhi MM (2019) Dynamic analysis of cracks under thermal shock considering thermoelasticity without energy dissipation. J Therm Stresses 42(5):607\u2013628","journal-title":"J Therm Stresses"},{"key":"1848_CR12","doi-asserted-by":"crossref","DOI":"10.1016\/j.tafmec.2020.102557","volume":"107","author":"MB Nazari","year":"2020","unstructured":"Nazari MB, Rokhi MM (2020) Evaluation of SIFs for cracks under thermal impact based on Green-Naghdi theory. Theoret Appl Fract Mech 107:102557","journal-title":"Theoret Appl Fract Mech"},{"key":"1848_CR13","doi-asserted-by":"crossref","DOI":"10.1016\/j.ijsolstr.2022.112090","volume":"264","author":"SH Bayat","year":"2023","unstructured":"Bayat SH, Nazari MB (2023) Dynamic crack propagation under thermal impact. Int J Solids Str 264:112090","journal-title":"Int J Solids Str"},{"issue":"1","key":"1848_CR14","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/S0022-5096(99)00029-0","volume":"48","author":"SA Silling","year":"2000","unstructured":"Silling SA (2000) Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 48(1):175\u2013209","journal-title":"J Mech Phys Solids"},{"issue":"1","key":"1848_CR15","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/s10704-018-0273-z","volume":"211","author":"Y Wang","year":"2018","unstructured":"Wang Y, Zhou X, Kou M (2018) A coupled thermo-mechanical bond-based peridynamics for simulating thermal cracking in rocks. Int J Fract 211(1):13\u201342","journal-title":"Int J Fract"},{"issue":"10","key":"1848_CR16","doi-asserted-by":"crossref","first-page":"11512","DOI":"10.1016\/j.ceramint.2018.03.214","volume":"44","author":"Y Wang","year":"2018","unstructured":"Wang Y, Zhou X, Kou M (2018) Peridynamic investigation on thermal fracturing behavior of ceramic nuclear fuel pellets under power cycles. Ceram Int 44(10):11512\u201311542","journal-title":"Ceram Int"},{"key":"1848_CR17","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/j.engfracmech.2018.08.028","volume":"204","author":"Y Wang","year":"2018","unstructured":"Wang Y, Zhou X, Kou M (2018) Numerical studies on thermal shock crack branching instability in brittle solids. Eng Fract Mech 204:157\u2013184","journal-title":"Eng Fract Mech"},{"key":"1848_CR18","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.ijrmms.2019.03.007","volume":"117","author":"Y Wang","year":"2019","unstructured":"Wang Y, Zhou X (2019) Peridynamic simulation of thermal failure behaviors in rocks subjected to heating from boreholes. Int J Rock Mech Min Sci 117:31\u201348","journal-title":"Int J Rock Mech Min Sci"},{"key":"1848_CR19","doi-asserted-by":"crossref","DOI":"10.1016\/j.mechmat.2019.103133","volume":"137","author":"Y Wang","year":"2019","unstructured":"Wang Y, Zhou X, Zhang T (2019) Size effect of thermal shock crack patterns in ceramics: Insights from a nonlocal numerical approach. Mech Mater 137:103133","journal-title":"Mech Mater"},{"key":"1848_CR20","doi-asserted-by":"crossref","first-page":"1284","DOI":"10.1016\/j.ijheatmasstransfer.2017.11.074","volume":"118","author":"L Wang","year":"2018","unstructured":"Wang L, Xu J, Wang J (2018) A peridynamic framework and simulation of non-Fourier and nonlocal heat conduction. Int J Heat Mass Transf 118:1284\u20131292","journal-title":"Int J Heat Mass Transf"},{"key":"1848_CR21","doi-asserted-by":"crossref","first-page":"706","DOI":"10.1016\/j.apm.2022.11.010","volume":"115","author":"Z Wen","year":"2023","unstructured":"Wen Z, Hou C, Zhao M, Wan X (2023) A peridynamic model for non-Fourier heat transfer in orthotropic plate with uninsulated cracks. Appl Math Model 115:706\u2013723","journal-title":"Appl Math Model"},{"issue":"1","key":"1848_CR22","doi-asserted-by":"crossref","first-page":"04017156","DOI":"10.1061\/(ASCE)EM.1943-7889.0001378","volume":"144","author":"XP Zhou","year":"2018","unstructured":"Zhou XP, Bi J (2018) Numerical simulation of thermal cracking in rocks based on general particle dynamics. J Eng Mech 144(1):04017156","journal-title":"J Eng Mech"},{"key":"1848_CR23","doi-asserted-by":"crossref","unstructured":"Rabczuk T, Song J, Zhuang X, Anitescu C (2019) Extended finite element and meshfree methods, Academic Press","DOI":"10.1016\/B978-0-12-814106-9.00011-5"},{"issue":"30","key":"1848_CR24","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1080\/14786435808565804","volume":"3","author":"AN Stroh","year":"1958","unstructured":"Stroh AN (1958) Dislocations and Cracks in Anisotropic Elasticity. Philos Mag 3(30):625\u2013646","journal-title":"Philos Mag"},{"issue":"3","key":"1848_CR25","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/BF00186854","volume":"1","author":"GC Sih","year":"1965","unstructured":"Sih GC, Paris PC, Irwin GR (1965) On cracks in rectilinearly anisotropic bodies. Int J FractMech 1(3):189\u2013203","journal-title":"Int J FractMech"},{"issue":"15","key":"1848_CR26","doi-asserted-by":"crossref","first-page":"2033","DOI":"10.1016\/S0013-7944(02)00258-8","volume":"70","author":"C Carloni","year":"2003","unstructured":"Carloni C, Piva A, Viola E (2003) An alternative complex variable formulation for an inclined crack in an orthotropic medium. Eng Fract Mech 70(15):2033\u20132058","journal-title":"Eng Fract Mech"},{"issue":"3","key":"1848_CR27","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1016\/j.compstruct.2004.03.020","volume":"68","author":"L Nobile","year":"2005","unstructured":"Nobile L, Carloni C (2005) Fracture analysis for orthotropic cracked plates. Compos Str 68(3):285\u2013293","journal-title":"Compos Str"},{"issue":"1","key":"1848_CR28","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/0013-7944(86)90209-2","volume":"25","author":"VE Saouma","year":"1986","unstructured":"Saouma VE, Sikiotis ES (1986) Stress intensity factors in anisotropic bodies using singular isoparametric elements. Eng Fract Mech 25(1):115\u2013121","journal-title":"Eng Fract Mech"},{"issue":"2","key":"1848_CR29","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/0013-7944(87)90166-4","volume":"27","author":"VE Saouma","year":"1987","unstructured":"Saouma VE, Ayari ML, Leavell DA (1987) Mixed mode crack propagation in homogeneous anisotropic solids. Eng Fract Mech 27(2):171\u2013184","journal-title":"Eng Fract Mech"},{"issue":"2","key":"1848_CR30","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/0013-7944(87)90196-2","volume":"26","author":"TJ Boone","year":"1987","unstructured":"Boone TJ, Wawrzynek PA, Ingraffea AR (1987) Finite element modeling of fracture propagation in orthotropic materials. Eng Fract Mech 26(2):185\u2013201","journal-title":"Eng Fract Mech"},{"issue":"5","key":"1848_CR31","doi-asserted-by":"crossref","first-page":"953","DOI":"10.1016\/0013-7944(90)90020-H","volume":"37","author":"M Doblare","year":"1990","unstructured":"Doblare M, Espiga F, Garcia L, Alcantud M (1990) Study of crack propagation in orthotropic materials by using the boundary element method. Eng Fract Mech 37(5):953\u2013967","journal-title":"Eng Fract Mech"},{"issue":"10","key":"1848_CR32","doi-asserted-by":"crossref","first-page":"1697","DOI":"10.1016\/S0266-3538(97)00240-6","volume":"58","author":"MH Aliabadi","year":"1998","unstructured":"Aliabadi MH, Sollero P (1998) Crack growth analysis in homogeneous orthotropic laminates. Compos Sci Technol 58(10):1697\u20131703","journal-title":"Compos Sci Technol"},{"issue":"6","key":"1848_CR33","doi-asserted-by":"crossref","first-page":"1412","DOI":"10.1016\/j.engfracmech.2007.07.021","volume":"75","author":"F Garc\u00eda-S\u00e1nchez","year":"2008","unstructured":"Garc\u00eda-S\u00e1nchez F, Zhang C, S\u00e1ez A (2008) A two-dimensional time-domain boundary element method for dynamic crack problems in anisotropic solids. Eng Fract Mech 75(6):1412\u20131430","journal-title":"Eng Fract Mech"},{"issue":"9","key":"1848_CR34","doi-asserted-by":"crossref","first-page":"1906","DOI":"10.1016\/j.engfracmech.2011.03.011","volume":"78","author":"SS Ghorashi","year":"2011","unstructured":"Ghorashi SS, Mohammadi S, Sabbagh-Yazdi S-R (2011) Orthotropic enriched element free Galerkin method for fracture analysis of composites. Eng Fract Mech 78(9):1906\u20131927","journal-title":"Eng Fract Mech"},{"key":"1848_CR35","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/j.icheatmasstransfer.2017.04.003","volume":"84","author":"J Zhang","year":"2017","unstructured":"Zhang J, Zhou G, Gong S, Wang S (2017) Transient heat transfer analysis of anisotropic material by using Element-Free Galerkin method. Int Commun Heat Mass Transfer 84:134\u2013143","journal-title":"Int Commun Heat Mass Transfer"},{"key":"1848_CR36","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1016\/j.enganabound.2019.01.011","volume":"101","author":"J-P Zhang","year":"2019","unstructured":"Zhang J-P, Wang S-S, Gong S-G, Zuo Q-S, Hu H-Y (2019) Thermo-mechanical coupling analysis of the orthotropic structures by using element-free Galerkin method. Eng Anal Bound Elem 101:198\u2013213","journal-title":"Eng Anal Bound Elem"},{"issue":"13","key":"1848_CR37","doi-asserted-by":"crossref","first-page":"1165","DOI":"10.1016\/j.finel.2006.05.001","volume":"42","author":"A Asadpoure","year":"2006","unstructured":"Asadpoure A, Mohammadi S, Vafai A (2006) Modeling crack in orthotropic media using a coupled finite element and partition of unity methods. Finite Elem Anal Des 42(13):1165\u20131175","journal-title":"Finite Elem Anal Des"},{"issue":"17","key":"1848_CR38","doi-asserted-by":"crossref","first-page":"3373","DOI":"10.1016\/j.engfracmech.2010.08.011","volume":"77","author":"D Motamedi","year":"2010","unstructured":"Motamedi D, Mohammadi S (2010) Dynamic analysis of fixed cracks in composites by the extended finite element method. Eng Fract Mech 77(17):3373\u20133393","journal-title":"Eng Fract Mech"},{"key":"1848_CR39","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/j.ijmecsci.2015.09.014","volume":"103","author":"L Bouhala","year":"2015","unstructured":"Bouhala L, Makradi A, Belouettar S (2015) Thermo-anisotropic crack propagation by XFEM. Int J Mech Sci 103:235\u2013246","journal-title":"Int J Mech Sci"},{"key":"1848_CR40","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1002\/nme.2411","volume":"77","author":"DBP Huynh","year":"2009","unstructured":"Huynh DBP, Belytschko T (2009) The extended finite element method for fracture in composite materials. Int J Numer Meth Eng 77:214\u2013239","journal-title":"Int J Numer Meth Eng"},{"key":"1848_CR41","doi-asserted-by":"publisher","DOI":"10.1007\/s10973-022-11549-4","author":"SH Bayat","year":"2022","unstructured":"Bayat SH, Nazari MB (2022) XFEM analysis of cracked orthotropic media under non-classic thermal shock. J Therm Anal Calorim. https:\/\/doi.org\/10.1007\/s10973-022-11549-4","journal-title":"J Therm Anal Calorim"},{"key":"1848_CR42","doi-asserted-by":"crossref","DOI":"10.1016\/j.euromechsol.2023.104913","volume":"99","author":"SH Bayat","year":"2023","unstructured":"Bayat SH, Nazari MB (2023) Dynamic crack analysis in anisotropic media under wave-like thermal loading. Eur J Mech A\/Solids 99:104913","journal-title":"Eur J Mech A\/Solids"},{"key":"1848_CR43","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1016\/j.compstruc.2014.09.017","volume":"147","author":"SS Ghorashi","year":"2015","unstructured":"Ghorashi SS, Valizadeh N, Mohammadi S, Rabczuk T (2015) T-spline based XIGA for fracture analysis of orthotropic media. Comput Str 147:138\u2013146","journal-title":"Comput Str"},{"key":"1848_CR44","volume":"176","author":"J Gu","year":"2019","unstructured":"Gu J, Yu T, Lich LV, Tanaka S, Qiu L, Bui TQ (2019) Adaptive orthotropic XIGA for fracture analysis of composites. Compos B Eng 176:107259","journal-title":"Compos B Eng"},{"key":"1848_CR45","doi-asserted-by":"crossref","first-page":"2150","DOI":"10.1002\/nme.1839","volume":"69","author":"A Asadpoure","year":"2007","unstructured":"Asadpoure A, Mohammadi S (2007) Developing new enrichment functions for crack simulation in orthotropic media by the extended finite element method. Int J Numer Meth Eng 69:2150\u20132172","journal-title":"Int J Numer Meth Eng"},{"key":"1848_CR46","doi-asserted-by":"crossref","DOI":"10.1016\/j.tafmec.2020.102843","volume":"112","author":"SH Bayat","year":"2021","unstructured":"Bayat SH, Nazari MB (2021) Thermal fracture analysis in orthotropic materials by XFEM. Theoret Appl Fract Mech 112:102843","journal-title":"Theoret Appl Fract Mech"},{"key":"1848_CR47","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/j.compstruct.2013.05.039","volume":"107","author":"L Cahill","year":"2014","unstructured":"Cahill L, Natarajan S, Bordas S, O\u2019Higgins R, McCarthy C (2014) An experimental\/numerical investigation into the main driving force for crack propagation in uni-directional fibre-reinforced composite laminae. Compos Str 107:119\u2013130","journal-title":"Compos Str"},{"key":"1848_CR48","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/j.engfracmech.2018.11.036","volume":"206","author":"MN Nguyen","year":"2019","unstructured":"Nguyen MN, Nguyen NT, Truong TT, Bui TQ (2019) Thermal-mechanical crack propagation in orthotropic composite materials by the extended four-node consecutive-interpolation element. Eng Fract Mech 206:89\u2013113","journal-title":"Eng Fract Mech"},{"issue":"4","key":"1848_CR49","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1007\/BF00018857","volume":"41","author":"KC Wu","year":"1989","unstructured":"Wu KC (1989) On the crack-tip fields of a dynamically propagating crack in an anisotropic elastic solid. Int J Fract 41(4):253\u2013266","journal-title":"Int J Fract"},{"issue":"1","key":"1848_CR50","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1023\/A:1007621500585","volume":"106","author":"K-C Wu","year":"2000","unstructured":"Wu K-C (2000) Dynamic crack growth in anisotropic material. Int J Fract 106(1):1\u201312","journal-title":"Int J Fract"},{"issue":"1","key":"1848_CR51","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/0020-7225(65)90021-2","volume":"3","author":"C Atkinson","year":"1965","unstructured":"Atkinson C (1965) The propagation of a brittle crack in anisotropic material. Int J Eng Sci 3(1):77\u201391","journal-title":"Int J Eng Sci"},{"key":"1848_CR52","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/0013-7944(95)00077-9","volume":"53","author":"KH Lee","year":"1996","unstructured":"Lee KH, Hawong J-S, Choi S-H (1996) Dynamic stress intensity factors KI, KII and dynamic crack propagation characteristics of orthotropic material. Eng Fract Mech 53:119\u2013140","journal-title":"Eng Fract Mech"},{"issue":"1","key":"1848_CR53","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/j.tafmec.2009.01.006","volume":"51","author":"X Gao","year":"2009","unstructured":"Gao X, Kang XW, Wang HG (2009) Dynamic crack tip fields and dynamic crack propagation characteristics of anisotropic material. Theoret Appl Fract Mech 51(1):73\u201385","journal-title":"Theoret Appl Fract Mech"},{"issue":"1","key":"1848_CR54","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s10704-009-9423-7","volume":"161","author":"D Motamedi","year":"2009","unstructured":"Motamedi D, Mohammadi S (2009) Dynamic crack propagation analysis of orthotropic media by the extended finite element method. Int J Fract 161(1):21\u201339","journal-title":"Int J Fract"},{"issue":"1","key":"1848_CR55","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/j.ijmecsci.2011.09.004","volume":"54","author":"D Motamedi","year":"2012","unstructured":"Motamedi D, Mohammadi S (2012) Fracture analysis of composites by time independent moving-crack orthotropic XFEM. Int J Mech Sci 54(1):20\u201337","journal-title":"Int J Mech Sci"},{"key":"1848_CR56","volume-title":"Thermal Stresses \u2013 Advanced Theory and Applications","author":"RB Hetnarski","year":"2009","unstructured":"Hetnarski RB, Eslami MR (2009) Thermal Stresses \u2013 Advanced Theory and Applications. Springer, Netherlands"},{"issue":"12","key":"1848_CR57","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1115\/1.3098984","volume":"51","author":"DS Chandrasekharaiah","year":"1998","unstructured":"Chandrasekharaiah DS (1998) Hyperbolic thermoelasticity: a review of recent literature. Appl Mech Rev 51(12):705\u2013729","journal-title":"Appl Mech Rev"},{"issue":"10","key":"1848_CR58","doi-asserted-by":"crossref","first-page":"2543","DOI":"10.1007\/s11012-018-0843-1","volume":"53","author":"YJ Yu","year":"2018","unstructured":"Yu YJ, Xue Z-N, Tian X-G (2018) A modified Green-Lindsay thermoelasticity with strain rate to eliminate the discontinuity. Meccanica 53(10):2543\u20132554","journal-title":"Meccanica"},{"key":"1848_CR59","first-page":"171","volume":"432","author":"A Green","year":"1991","unstructured":"Green A, Naghdi PM (1991) A re-examination of the basic postulates of thermomechanics. Proc Royal Soc London Series A 432:171\u2013194","journal-title":"Proc Royal Soc London Series A"},{"issue":"1","key":"1848_CR60","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/BF01262690","volume":"13","author":"BD Coleman","year":"1963","unstructured":"Coleman BD, Noll W (1963) The thermodynamics of elastic materials with heat conduction and viscosity. Arch Ration Mech Anal 13(1):167\u2013178","journal-title":"Arch Ration Mech Anal"},{"key":"1848_CR61","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1080\/014957399280977","volume":"22","author":"R Quintanilla","year":"1999","unstructured":"Quintanilla R (1999) On the spatial behavior in thermoelasticity without energy dissipation. J Therm Stresses 22:213\u2013224","journal-title":"J Therm Stresses"},{"key":"1848_CR62","doi-asserted-by":"crossref","unstructured":"Kaw AK (2005) Mechanics of Composite Materials (2nd Ed.), CRC Press","DOI":"10.1201\/9781420058291"},{"key":"1848_CR63","doi-asserted-by":"crossref","first-page":"2802","DOI":"10.1016\/j.engfracmech.2006.04.015","volume":"73","author":"S Dag","year":"2006","unstructured":"Dag S (2006) Thermal fracture analysis of orthotropic functionally graded materials using an equivalent domain integral approach. Eng Fract Mech 73:2802\u20132828","journal-title":"Eng Fract Mech"},{"key":"1848_CR64","doi-asserted-by":"crossref","unstructured":"Khoei AR (2014) Extended finite element method: theory and applications. Wiley","DOI":"10.1002\/9781118869673"},{"issue":"6","key":"1848_CR65","doi-asserted-by":"crossref","first-page":"1093","DOI":"10.1016\/0013-7944(90)90137-6","volume":"35","author":"SJ Chu","year":"1990","unstructured":"Chu SJ, Hong CS (1990) Application of the Jk integral to mixed mode crack problems for anisotropic composite laminates. Eng Fract Mech 35(6):1093\u20131103","journal-title":"Eng Fract Mech"},{"issue":"15","key":"1848_CR66","doi-asserted-by":"crossref","first-page":"3967","DOI":"10.1016\/S0020-7683(03)00176-8","volume":"40","author":"J-H Kim","year":"2003","unstructured":"Kim J-H, Paulino GH (2003) The interaction integral for fracture of orthotropic functionally graded materials: evaluation of stress intensity factors. Int J Solids Str 40(15):3967\u20134001","journal-title":"Int J Solids Str"},{"key":"1848_CR67","doi-asserted-by":"crossref","unstructured":"Bayat SH, Nazari MB (2023) Dynamically propagating cracks in anisotropic plates subjected to hyperbolic thermal shock. Adv Mater Process Technol pp. 1\u201333","DOI":"10.1080\/2374068X.2023.2204034"},{"issue":"2","key":"1848_CR68","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1115\/1.3601206","volume":"35","author":"JR Rice","year":"1968","unstructured":"Rice JR (1968) A path independent integral and the approximate analysis of strain concentration by notches and cracks. J Appl Mech 35(2):379\u2013386","journal-title":"J Appl Mech"},{"issue":"3","key":"1848_CR69","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1007\/BF00032831","volume":"12","author":"M Stern","year":"1976","unstructured":"Stern M, Becker EB, Dunham RS (1976) A contour integral computation of mixed-mode stress intensity factors. Int J Fract 12(3):359\u2013368","journal-title":"Int J Fract"},{"issue":"2","key":"1848_CR70","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1115\/1.3153665","volume":"47","author":"JF Yau","year":"1980","unstructured":"Yau JF, Wang SS, Corten HT (1980) A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity. J Appl Mech 47(2):335\u2013341","journal-title":"J Appl Mech"},{"key":"1848_CR71","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1007\/BF00013381","volume":"16","author":"S Wang","year":"1980","unstructured":"Wang S, Yau J, Corten HT (1980) A mixed-mode crack analysis of rectilinear anisotropic solids using conservation laws of elasticity. Int J Fract 16:247\u2013259","journal-title":"Int J Fract"},{"issue":"2","key":"1848_CR72","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1016\/0013-7944(85)90029-3","volume":"21","author":"FZ Li","year":"1985","unstructured":"Li FZ, Shih CF, Needleman A (1985) A comparison of methods for calculating energy release rates. Eng Fract Mech 21(2):405\u2013421","journal-title":"Eng Fract Mech"},{"issue":"9","key":"1848_CR73","doi-asserted-by":"crossref","first-page":"2557","DOI":"10.1016\/S0020-7683(02)00114-2","volume":"39","author":"JE Dolbow","year":"2002","unstructured":"Dolbow JE, Gosz M (2002) On the computation of mixed-mode stress intensity factors in functionally graded materials. Int J Solids Struct 39(9):2557\u20132574","journal-title":"Int J Solids Struct"},{"issue":"5","key":"1848_CR74","doi-asserted-by":"crossref","first-page":"827","DOI":"10.1002\/nme.2197","volume":"74","author":"M Duflot","year":"2008","unstructured":"Duflot M (2008) The extended finite element method in thermoelastic fracture mechanics. Int J Numer Meth Eng 74(5):827\u2013847","journal-title":"Int J Numer Meth Eng"},{"key":"1848_CR75","doi-asserted-by":"crossref","DOI":"10.1016\/j.tafmec.2019.102359","volume":"104","author":"E Mohtarami","year":"2019","unstructured":"Mohtarami E, Baghbanan A, Hashemolhosseini H, Bordas SP (2019) Fracture mechanism simulation of inhomogeneous anisotropic rocks by extended finite element method. Theoret Appl Fract Mech 104:102359","journal-title":"Theoret Appl Fract Mech"},{"issue":"6","key":"1848_CR76","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1002\/(SICI)1097-0207(19990228)44:6<767::AID-NME524>3.0.CO;2-G","volume":"44","author":"P Krysl","year":"1999","unstructured":"Krysl P, Belytschko T (1999) The Element Free Galerkin method for dynamic propagation of arbitrary 3-D cracks. Int J Numer Meth Eng 44(6):767\u2013800","journal-title":"Int J Numer Meth Eng"},{"issue":"16","key":"1848_CR77","doi-asserted-by":"crossref","first-page":"4830","DOI":"10.1016\/j.ijsolstr.2005.06.102","volume":"43","author":"SH Song","year":"2006","unstructured":"Song SH, Paulino GH (2006) Dynamic stress intensity factors for homogeneous and smoothly heterogeneous materials using the interaction integral method. Int J Solids Str 43(16):4830\u20134866","journal-title":"Int J Solids Str"},{"issue":"5","key":"1848_CR78","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1002\/nme.1283","volume":"63","author":"J R\u00e9thor\u00e9","year":"2005","unstructured":"R\u00e9thor\u00e9 J, Gravouil A, Combescure A (2005) An energy-conserving scheme for dynamic crack growth using the eXtended finite element method. Int J Numer Meth Eng 63(5):631\u2013659","journal-title":"Int J Numer Meth Eng"},{"key":"1848_CR79","doi-asserted-by":"crossref","unstructured":"Anderson TL (2017) Fracture mechanics: fundamentals and applications, CRC press","DOI":"10.1201\/9781315370293"},{"issue":"4","key":"1848_CR80","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1090\/qam\/1031687","volume":"47","author":"C Dongye","year":"1989","unstructured":"Dongye C, Ting TCT (1989) Explicit expressions of Barnett-Lothe tensors and their associated tensors for orthotropic materials. Q Appl Math 47(4):723\u2013234","journal-title":"Q Appl Math"},{"issue":"1\u20133","key":"1848_CR81","doi-asserted-by":"crossref","first-page":"516","DOI":"10.1016\/j.cma.2006.05.010","volume":"196","author":"S Bargmann","year":"2006","unstructured":"Bargmann S, Steinmann P (2006) Theoretical and computational aspects of non-classical thermoelasticity. Comput Methods Appl Mech Eng 196(1\u20133):516\u2013527","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"2","key":"1848_CR82","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1115\/1.3173686","volume":"55","author":"T-C Chen","year":"1988","unstructured":"Chen T-C, Weng C-I (1988) Generalized coupled transient thermoelastic plane problems by laplace transform\/finite element method. J Appl Mech 55(2):377\u2013382","journal-title":"J Appl Mech"},{"issue":"1","key":"1848_CR83","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1016\/0045-7949(90)90296-E","volume":"34","author":"KK Tamma","year":"1990","unstructured":"Tamma KK, Railkar SB (1990) Evaluation of thermally induced non-fourier stress wave disturbances via tailored hybrid transfinite element formulations. Comput Str 34(1):5\u201316","journal-title":"Comput Str"},{"issue":"3","key":"1848_CR84","doi-asserted-by":"crossref","first-page":"534","DOI":"10.2514\/2.993","volume":"38","author":"PH Tehrani","year":"2000","unstructured":"Tehrani PH, Eslami MR (2000) Boundary element analysis of coupled thermoelasticity with relaxation times in finite domain. AIAA J 38(3):534\u2013541","journal-title":"AIAA J"},{"key":"1848_CR85","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.ijmecsci.2014.03.009","volume":"82","author":"SM Hosseini","year":"2014","unstructured":"Hosseini SM, Sladek J, Sladek V (2014) Two dimensional transient analysis of coupled non-Fick diffusion\u2013thermoelasticity based on Green-Naghdi theory using the meshless local Petrov-Galerkin (MLPG) method. Int J Mech Sci 82:74\u201380","journal-title":"Int J Mech Sci"},{"issue":"2","key":"1848_CR86","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/BF00370063","volume":"9","author":"KK Tamma","year":"1992","unstructured":"Tamma KK, Namburu RR (1992) An effective finite element modeling\/analysis approach for dynamic thermoelasticity due to second sound effects. Comput Mech 9(2):73\u201384","journal-title":"Comput Mech"},{"key":"1848_CR87","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1016\/j.ijmecsci.2017.07.008","volume":"131\u2013132","author":"C Li","year":"2017","unstructured":"Li C, Guo H (2017) Time-domain finite element analysis to nonlinear transient responses of generalized diffusion-thermoelasticity with variable thermal conductivity and diffusivity. Int J Mech Sci 131\u2013132:234\u2013244","journal-title":"Int J Mech Sci"},{"key":"1848_CR88","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1080\/01495739.2016.1217179","volume":"40","author":"Y Kiani","year":"2017","unstructured":"Kiani Y, Eslami MR (2017) A GDQ approach to thermally nonlinear generalized thermoelasticity of disks. J Therm Stresses 40:121\u2013133","journal-title":"J Therm Stresses"},{"issue":"3","key":"1848_CR89","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1061\/JMCEA3.0000098","volume":"85","author":"NM Newmark","year":"1959","unstructured":"Newmark NM (1959) A method of computation for structural dynamics. J Eng Mech Div 85(3):67\u201394","journal-title":"J Eng Mech Div"},{"issue":"3","key":"1848_CR90","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1016\/j.cma.2016.05.013","volume":"308","author":"L Wen","year":"2016","unstructured":"Wen L, Tian R (2016) Improved XFEM: Accurate and robust dynamic crack growth simulation. Comput Methods Appl Mech Eng 308(3):256\u2013285","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1848_CR91","volume-title":"Dynamics of Structures","author":"AK Chopra","year":"2017","unstructured":"Chopra AK (2017) Dynamics of Structures. University of California at Berkeley, Pearson"},{"issue":"4","key":"1848_CR92","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1115\/1.3656897","volume":"85","author":"F Erdogan","year":"1963","unstructured":"Erdogan F, Sih GC (1963) On the crack extension in plates under plane loading and transverse shear. J Basic Eng 85(4):519\u2013525","journal-title":"J Basic Eng"},{"key":"1848_CR93","doi-asserted-by":"crossref","DOI":"10.1016\/j.tafmec.2021.102946","volume":"113","author":"M Nejati","year":"2021","unstructured":"Nejati M, Bahrami B, Ayatollahi MR, Driesner T (2021) On the anisotropy of shear fracture toughness in rocks. Theoret Appl Fract Mech 113:102946","journal-title":"Theoret Appl Fract Mech"},{"key":"1848_CR94","unstructured":"\u202cGdoutos E (2005) Fracture mechanics: An Introduction, Springer"},{"key":"1848_CR95","doi-asserted-by":"crossref","first-page":"424","DOI":"10.1016\/j.compstruct.2018.10.083","volume":"209","author":"Natarajan S Hirshikesh","year":"2019","unstructured":"Hirshikesh Natarajan S, Annabattula RK (2019) \"Modeling crack propagation in variable stiffness composite laminates using the phase field method. Comp Str 209:424\u2013433","journal-title":"Comp Str"},{"issue":"3","key":"1848_CR96","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1007\/BF00017973","volume":"27","author":"JF Kalthoff","year":"1985","unstructured":"Kalthoff JF (1985) On the measurement of dynamic fracture toughnesses \u2014 a review of recent work. Int J Fract 27(3):277\u2013298","journal-title":"Int J Fract"},{"issue":"12","key":"1848_CR97","doi-asserted-by":"crossref","first-page":"1873","DOI":"10.1002\/nme.941","volume":"58","author":"T Belytschko","year":"2003","unstructured":"Belytschko T, Chen H, Xu J, Zi G (2003) Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment. Int J Numer Meth Eng 58(12):1873\u20131905","journal-title":"Int J Numer Meth Eng"},{"key":"1848_CR98","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511546761","volume-title":"Dynamic Fracture Mechanics","author":"L Freund","year":"1990","unstructured":"Freund L (1990) Dynamic Fracture Mechanics. Cambridge University Press, Cambridge"},{"issue":"1","key":"1848_CR99","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1007\/s10704-009-9405-9","volume":"162","author":"T Menouillard","year":"2010","unstructured":"Menouillard T, Song J-H, Duan Q (2010) Time dependent crack tip enrichment for dynamic crack propagation. Int J Fract 162(1):33\u201349","journal-title":"Int J Fract"}],"container-title":["Engineering with Computers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-023-01848-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00366-023-01848-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-023-01848-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,20]],"date-time":"2024-04-20T22:50:15Z","timestamp":1713653415000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00366-023-01848-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,25]]},"references-count":99,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,4]]}},"alternative-id":["1848"],"URL":"https:\/\/doi.org\/10.1007\/s00366-023-01848-1","relation":{},"ISSN":["0177-0667","1435-5663"],"issn-type":[{"value":"0177-0667","type":"print"},{"value":"1435-5663","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,6,25]]},"assertion":[{"value":"20 December 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 May 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 June 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}